Lower bounds and dense discontinuity phenomena for the stabilizability radius of linear switched systems

Carl P Dettmann; Raphael M Jungers; Paolo Mason

doi:10.1016/j.sysconle.2020.104737

Lower bounds and dense discontinuity phenomena for the stabilizability radius of linear switched systems

Carl P Dettmann ^*, Raphael M Jungers, Paolo Mason^*

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

Abstract

We investigate the stabilizability of discrete-time linear switched systems, when the sole control action of the controller is the switching signal, and when the controller has access to the state of the system in real time. Despite their apparent simplicity, determining if such systems are stabilizable appears to be a very challenging problem, and basic examples have been known for long, for which the stabilizability question is open. We provide new results allowing us to bound the so-called stabilizability radius, which characterizes the stabilizability property of discrete-time linear switched systems. These results allow us to compute significantly improved explicit lower bounds on the stabilizability radius for the above-mentioned examples. As a by-product, we exhibit a discontinuity property for this problem, which brings theoretical understanding of its complexity.

Original language	English
Article number	104737
Number of pages	6
Journal	Systems and Control Letters
Volume	142
Early online date	29 Jun 2020
DOIs	https://doi.org/10.1016/j.sysconle.2020.104737
Publication status	Published - 1 Aug 2020

Keywords

Switched systems
stabilizability
joint spectral characteristics 2010 MS

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abstract = "We investigate the stabilizability of discrete-time linear switched systems, when the sole control action of the controller is the switching signal, and when the controller has access to the state of the system in real time. Despite their apparent simplicity, determining if such systems are stabilizable appears to be a very challenging problem, and basic examples have been known for long, for which the stabilizability question is open. We provide new results allowing us to bound the so-called stabilizability radius, which characterizes the stabilizability property of discrete-time linear switched systems. These results allow us to compute significantly improved explicit lower bounds on the stabilizability radius for the above-mentioned examples. As a by-product, we exhibit a discontinuity property for this problem, which brings theoretical understanding of its complexity.",

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AU - Jungers, Raphael M

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N2 - We investigate the stabilizability of discrete-time linear switched systems, when the sole control action of the controller is the switching signal, and when the controller has access to the state of the system in real time. Despite their apparent simplicity, determining if such systems are stabilizable appears to be a very challenging problem, and basic examples have been known for long, for which the stabilizability question is open. We provide new results allowing us to bound the so-called stabilizability radius, which characterizes the stabilizability property of discrete-time linear switched systems. These results allow us to compute significantly improved explicit lower bounds on the stabilizability radius for the above-mentioned examples. As a by-product, we exhibit a discontinuity property for this problem, which brings theoretical understanding of its complexity.

AB - We investigate the stabilizability of discrete-time linear switched systems, when the sole control action of the controller is the switching signal, and when the controller has access to the state of the system in real time. Despite their apparent simplicity, determining if such systems are stabilizable appears to be a very challenging problem, and basic examples have been known for long, for which the stabilizability question is open. We provide new results allowing us to bound the so-called stabilizability radius, which characterizes the stabilizability property of discrete-time linear switched systems. These results allow us to compute significantly improved explicit lower bounds on the stabilizability radius for the above-mentioned examples. As a by-product, we exhibit a discontinuity property for this problem, which brings theoretical understanding of its complexity.

KW - Switched systems

KW - stabilizability

KW - joint spectral characteristics 2010 MS

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DO - 10.1016/j.sysconle.2020.104737

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JO - Systems and Control Letters

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